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Let \(\mu \)  be a measure on \((X,\mathfrak {M})\)  and \(K\) 
be a Markov kernel from \((X,\mathfrak {M})\)  to \((Y,\mathfrak {N})\) .
Then define the measure \(\gamma \)  by how it acts on measurable functions \(f(x,y)\)  in \((\mathfrak {M}\otimes \mathfrak {N})_+\)  in the following way:
\(\gamma f=\int _X d\mu (x)\int _Y f(x,y) K(x,dy).\) 
